Method for finding signal direction using modal antenna

ABSTRACT

A method for obtaining the direction of a signal incoming to a communication device is provided using a modal antenna that has multiple modes corresponding to multiple radiation patterns with a single feed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of priority with U.S. Provisional Ser. No. 61/954,506, filed Mar. 17, 2014, titled “METHOD FOR FINDING SIGNAL'S DIRECTION USING MODAL ANTENNA”; the contents of which are hereby incorporated by reference.

BACKGROUND

Field of the Invention

This invention relates generally to wireless communications; and more particularly, to methods for finding direction of a signal using an active multi-mode antenna.

Description of the Related Art

As new generations of wireless communication devices become smaller and embedded with increased applications, new antenna designs, system configurations and controlling algorithms are required to enable new capabilities and to improve QOS. For example, geolocation is a function to identify the geographic location of a mobile device, such as a cellular phone, a smart phone, a laptop, a tablet, an internet-connected computer terminal and other wireless communication device. These devices are expected to incorporate the location-determining function because of emergency “911” services, public safety and law enforcement concerns. Furthermore, in the emerging vehicle-to-vehicle communication protocols, the location-determining function enables one car to steer the communication signal following the movement of the other car, thereby improving the quality of the communication link and reducing electromagnetic interferences. Such geolocation or location-determining functions can be achieved by configuring an antenna system to find the direction of RF signals.

Direction finding, a.k.a. the angel of arrival (AOA) estimation, generally refers to a method of determining the direction of arrival of incoming signals, and plays an important role in spectrum monitoring as well as in reconnaissance and surveillance applications. Typically, the direction finding utilizes an array of antennas that detect incoming RF signals, wherein phase and amplitude information is correlated to calculate the direction of arrival of the signals. In such a conventional direction finding system, one receiver is provided for each antenna, in particular when high resolution is needed in situations where multipath interferences or co-channel signals exist. This configuration allows for continuous sampling of information received by each antenna. However, the drawback is that it is costly and requisite of a large space to provide multiple antennas and receive chains. As is typically the case when a multi-antenna system is used, electromagnetic coupling among the antennas as well as between the antennas and nearby electronics often deteriorates transmission and reception qualities. Additionally, efficiency may deteriorate in many instances where multiple RF chains are energized and power consumption increases.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example of a modal antenna.

FIG. 2(a) illustrates a radiation pattern associated with the modal antenna of FIG. 1 in the first state.

FIG. 2(b) illustrates a radiation pattern associated with the modal antenna of FIG. 1 in the second state.

FIG. 3 is a flowchart illustrating a first direction finding algorithm to obtain the angle that gives the minimum of Err(Θ,Φ) as the AOA of the signal.

FIG. 4 is a flowchart illustrating a second direction finding algorithm to obtain the angle that gives the minimum of Err^(K)(Θ,Φ) as the AOA of the signal for the K-th mode, where the angle (Θ,Φ) is selected from a limited set of angles that satisfy certain criteria.

FIG. 5 is a flowchart illustrating the procedure for taking signal strength changes into account.

FIG. 6 is a flowchart illustrating the procedure for taking signal strength changes into account, which can be incorporated in the second algorithm.

FIG. 7 illustrates an example schematically showing multipath signals and a communication device receiving them.

FIG. 8 is a flowchart illustrating an algorithm in which multipath components are utilized to enhance the accuracy, or the confidence level, of the AOA estimation in the first algorithm.

FIG. 9 is a flowchart illustrating an algorithm in which multipath components are utilized to enhance the accuracy, or the confidence level, of the AOA estimation in the second algorithm.

FIG. 10 is a flowchart illustrating the process of updating the gain variations based on the AOA information previously obtained.

FIG. 11 is a table illustrating an example of gain variations and signal strength variations used for the decision making.

FIG. 12 schematically illustrates the measurement of the phase shift of the signal strength during the transition between modes of the antenna.

FIG. 13 illustrates a portion of the look-up table showing the phase data of the gain according to the angles and the modes, i.e., radiation patterns of the antenna.

DETAILED DESCRIPTION

In view of the above problems associate with direction finding based on a multi-antenna system, this document provides a new type of direction finding methods based on a single antenna capable of producing multiple radiations patterns.

A modal antenna, also referred to as a null-steering antenna, can generate multiple modes corresponding to multiple radiation patterns, equivalent to having a set of antennas with the same feed. By using the modal antenna capable of generating different radiation patterns, it is possible to exploit a priori knowledge of antenna nulls and lobes in the different modes for steering the beam to have nulls in dominant interference directions while keeping gain in desired directions. Accordingly, implementation of a modal antenna may allow for pattern diversity with one antenna, thereby requiring less volume and area than using multiple antennas. Examples of structures and implementations of the modal antennas are provided in U.S. Pat. No. 7,911,402, entitled “ANTENNA AND METHOD FOR STEERING ANTENNA BEAM DIRECTION,” issued on Mar. 22, 2011; the contents of the which are hereby incorporated by reference and are summarized as follows:

FIG. 1 illustrates an example of a modal antenna 100, which includes an Isolated Magnetic Dipole™ (IMD) element 104 placed on a ground plane 108, a first parasitic element 112 coupled to an first active element 113, and a second parasitic element 116 coupled to a second active element 117. The active elements 113 and 117 may include switches that either electrically connect (short) or disconnect (open) the parasitic elements 112 and 116 to the ground plane 108. This structure allows for two different modes of operation with a common frequency corresponding to a first state where the parasitic elements 112 and 116 are shorted to the ground and a second state where the parasitic elements 112 and 116 are open.

FIG. 2(a) illustrates a radiation pattern 204 associated with the antenna 100 in the first state; and FIG. 2(b) illustrates a radiation pattern 208 in the second state, which shows a ninety-degree shift in direction as compared to the radiation pattern 204. Thus, by controlling the active elements 113 and 117 of the modal antenna 100, the operation of two modes can be obtained at the same frequency. The control scheme can be extended for three or more multi-mode operations by incorporating, for example, tunable elements in the active elements for variable control and additional active elements for matching. Examples of these active elements include switches, tunable capacitors, tunable phase shifters, diodes, micro-electro-mechanical system (MEMS) switches, MEMS tunable capacitors, and transistors including a metal oxide semiconductor field effect transistor (MOSFET), a metal semiconductor field effect transistor (MESFET), a pseudomorphic high electron mobility transistor (pHEMT), a heterojunction bipolar transistor (HBT) or of other suitable technologies.

Direction finding algorithms according to embodiments, to estimate the angle of arrival (AOA) of RF signals by using a modal antenna having multiple radiations patterns, are explained below with reference to the subsequent figures.

In these algorithms, the modal antenna is configured to have multiple (N) antenna modes, corresponding to multiple radiation patterns K=0, 1 . . . and N−1; i.e. the modal antenna produces a distinct radiation pattern in each distinct antenna mode of the N modes. The spherical coordinate is used to estimate the AOA of the signal, which is denoted as (Θ₀, Φ₀). The (Θ,Φ)-space is spanned prior to the direction finding procedure, and all possible discrete values of Θ and Φ to consider according to the required resolution are listed in the group, or a set, Set{Θ,Φ}. G^(K)(Θ,Φ) denotes the gain in dB of the modal antenna with the K-th radiation pattern at the angle (Θ,Φ), which can be premeasured and stored in a memory. E^(K)(Θ,Φ) denotes the difference in gain in dB between the current mode having the K-th radiation pattern and the previous mode having the (K−1)-th radiation pattern at the angle (Θ, Φ), and is defined as follows: E ^(K)(Θ,Φ)=G ^(K)(Θ,Φ)−G ^(K−1)(Θ,Φ),   Eq. (1) where K=1, 2 . . . and N, and EN(Θ,Φ) is defined as [G0(Θ,Φ)−GN−1(Θ,Φ)]. S^(K) denotes the signal strength in dBm in the configuration with the K-th radiation pattern, where K=0, 1 . . . and N−1. Δ^(K) denotes the difference in signal strength in dB between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern, and is defined as follows: Δ^(K) =S ^(K) −S ^(K−1),   Eq. (2) where K=1, 2 . . . and N, and Δ^(N) is defined as [S⁰−S^(N−1)].

Having defined the above parameters, computation can be made to obtain the difference between the gain variation E^(K)(Θ,Φ) and the signal strength variation Δ^(K) at each angle (Θ, Φ) as follows: Err^(K)(Θ,Φ)=[E ^(K)(Θ,Φ)−Δ^(K)]²,  Eq. (3) where K=1, 2 . . . and N, and the power of 2 is taken for having a positive number for the sake of computational convenience. Accordingly, the contributions from all configurations with different radiation patterns can be obtained as follows: Err(Θ,Φ)=Σ_(K=1) ^(N)Err^(K)(Θ,Φ).  Eq. (4) Therefore, the AOA (Θ₀, Φ₀) of the signal may be obtained by finding the minimum of the above quantity in Eq. (4) over all pairs of (Θ, Φ) in Set{Θ,Φ} as follows: Err(Θ₀,Φ₀)=min[Err(Θ,Φ)],  Eq. (5) where (Θ₀, Φ₀) ϵ Set{Θ,Φ}.

FIG. 3 is a flowchart illustrating a first direction finding algorithm to obtain the angle that gives the minimum of Err(Θ,Φ) as the AOA of the signal according to the above procedure. The initialization is carried out in step 304, to set the mode, i.e., the radiation pattern of the modal antenna, to be K=0. Additionally, in this step, the discrete values of (Θ, Φ) to span in the spherical coordinate are determined according to the required resolution, and stored in Set{Θ,Φ}. In step 308, the signal strength in the configuration with the 0-th radiation pattern, S⁰, is measured. Steps 312-328 represent the do-loop to compute Err^(K)(Θ,Φ) iteratively from K=1 to K=N. Specifically, after the radiation pattern is changed to the next pattern in step 312, the signal strength in the new configuration with the K-th radiation pattern, S^(K), is measured in step 316. Using the previous measurement value S^(K−1), the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern, i.e., the signal strength variation, can be computed as in Eq. (2), i.e., Δ^(K)=S^(K)−S^(K−1), in step 320. Using the measured signal strength variation Δ^(K) and the premeasured and stored G^(K)(Θ, Φ) value, which is the gain of the modal antenna at the angle (Θ,Φ) when the K-th radiation pattern is selected, step 324 proceeds to compute Err^(K)(Θ,Φ) as in Eq. (3), i.e., Err^(K)(Θ,Φ)=[E^(K)(Θ,Φ)−Δ^(K)]², where E^(K)(Θ, Φ)=G^(K)(Θ,Φ)−G^(K−1)(Θ,Φ) which is the gain variation, as in Eq. (1). In step 324, this computation is carried out for each pair of (Θ, Φ) values in Set{Θ,Φ}. After the computation of Err^(K)(Θ,Φ) for each pair of (Θ, Φ) values for K=1 through N, in step 332, Err^(K)(Θ,Φ) for all configurations with different radiation patterns is summed as in Eq. (4) to obtain Err(Θ,Φ) for each pair of (Θ, Φ) values in Set{Θ,Φ}. In step 336, among Err(Θ, Φ) values for all pairs of (Θ, Φ) in Set{Θ,Φ}, Err(Θ,Φ) that gives the minimum is found. If the process is determined to be terminated in step 340, the (Θ, Φ) value that gives the minimum Err(Θ,Φ) is outputted as the AOA (Θ₀, Φ₀) in step 344. If the process is determined to be continued in step 340, the process goes back to step 304 for initialization, and the subsequent steps are repeated.

In the above algorithm, the AOA (Θ₀, Φ₀) is obtained as the angle that gives the minimum of Err(Θ,Φ) over all pairs of (Θ, Φ) in Set{Θ,Φ}. Alternatively, the AOA (Θ₀, Φ₀) may be obtained as the angle that gives the minimum of Err^(K)(Θ,Φ) for the configuration with the K-th radiation pattern, except that the pair of (Θ, Φ) is selected from a limited set of angles that satisfy certain criteria.

FIG. 4 is a flowchart illustrating a second direction finding algorithm to obtain the angle that gives the minimum of Err^(K)(Θ,Φ) as the AOA of the signal for the K-th mode, where the angle (Θ,Φ) is selected from a limited set of angles that satisfy certain criteria. The initialization is carried out in step 404, to set the mode, i.e., the radiation pattern of the modal antenna, to be K=0. Additionally, in this step, the discrete values of (Θ, Φ) to span in the spherical coordinate are determined according to certain criteria, and stored in Subset{Θ,Φ}. The angles (Θ,Φ) in the initial Subset{Θ,Φ} may be selected from the original Set{Θ,Φ} according to an empirical judgment based on the prior computational results or measured data or other sound engineering judgment. In step 408, the signal strength in the configuration with the 0-th radiation pattern, S⁰, is measured. Steps 412-464 represent the do-loop to compute Err^(K)(Θ,Φ) iteratively from K=1 to K=N. After the radiation pattern is changed to the next pattern in step 412, the signal strength in the new configuration with the K-th radiation pattern, S^(K), is measured in step 416. Using the previous measurement value S^(K−1), the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern, i.r., the signal strength variation, can be computed as in Eq. (2), i.e., Δ^(K)=S^(K)−S^(K−1), in step 420. In step 424, the first pair of (Θ, Φ) is selected from Subset{Θ,Φ}. Using the measured signal strength variation Δ^(K) and the premeasured and stored G^(K)(Θ, Φ) value, which is the gain of the modal antenna at the angle (Θ,Φ) when the K-th radiation pattern is selected, step 428 proceeds to compute Err^(K)(Θ,Φ) as in Eq. (3), i.e., Err^(K)(Θ,Φ)=[E^(K)(Θ,Φ)−Δ^(K)]², where E^(K)(Θ,Φ)=G^(K)(Θ,Φ)−G^(K−1)(Θ,Φ), which is the gain variation, as in Eq. (1). After the computation of Err^(K)(Θ,Φ) for the pair of (Θ, Φ), it is judged in step 436 if the Err^(K)(Θ, Φ) value is smaller than a predetermined threshold, Tshld, which is related to a tolerance in judging the accuracy of the final AOA. If Yes, in step 440, the angle (Θ, Φ) that gives the relationship, Err^(K)(Θ, Φ)<Tshld, is stored in Temp-Subset{Θ,Φ}. If No in step 436 as well as after step 440, the process proceeds to step 444, where it is judged if all the angles (Θ, Φ) in Subset{Θ,Φ} have been exhausted. If No in step 444, the next pair of angles (Θ,Φ) in Subset{Θ,Φ} is selected in step 432, and the process from step 428 through step 432 is repeated until all the angles (Θ,Φ) in Subset{Θ,Φ} are exhausted. In step 448, Subset{Θ,Φ} is replaced with Temp-Subset{Θ,Φ}, which means only the angles (Θ,Φ) that satisfy the relationship, Err^(K)(Θ, Φ)<Tshld, are selected and stored as the updated Subset{Θ,Φ}. In step 452, among Err^(K)(Θ, Φ) values for all pairs of (Θ, Φ) in Subset{Θ,Φ}, Err(Θ,Φ) that gives the minimum is found. If the process is determined to be terminated in step 456, the (Θ, Φ) value that gives the minimum Err^(K) (Θ,Φ) is outputted as the AOA (Θ₀, Φ₀) for the given K in step 460. If the process is determined to be continued in step 456, the process goes to step 464 to judge if K=N has been reached. If No, the next K is selected in 412 and the process at step 416 and afterward is repeated. If Yes, the process goes back to step 404 for initialization, and the subsequent step are repeated.

In the above first and second algorithms, the E^(K)(Θ,Φ) values are obtained by using the gain values of the modal antenna, G^(K)(Θ,Φ), which can be premeasured and stored in the memory. In addition to the antenna gain in free space, antenna gains under various use conditions or environments can also be premeasured and stored in the memory. For example, the radiation patterns may be disturbed because of placement of a head, a hand, laps, wood, metal, or other interference-causing objects, with different positions and angles, in the proximity of the antenna. The antenna gains under such different conditions or environments can be premeasured and stored in the memory. Furthermore, one or more sensors may be included in the device to detect the use conditions or environments. Such sensors may include a proximity sensor, a motion sensor, a light sensor, a pressure sensor or other types of sensors. During the actual operation, the sensor is configured to detect the use condition or the environment during each time interval, and send the detected information to a controller, which is configured to select the gain values corresponding to the detected condition or environment. These premeasured G^(K)(Θ,Φ) values that are stored in the memory according to conditions or environments can then be used to obtain the E^(K)(Θ,Φ) values in the first and second algorithms.

In the actual application of the above two algorithms, there is a possibility that the actual signal strength changes during the time between measurements for the configurations with the K-th and (K−1)-th radiation patterns, giving rise to an inaccurate estimation of the AOA. To take into account such changes, the signal strength can be measured over a predetermined time period, and the time average of the signal strength can be used in the direction finding algorithms. FIG. 5 is a flowchart illustrating the procedure for taking signal strength changes into account, which can be incorporated in each of the first and second algorithms described with reference to FIGS. 3 and 4, respectively. After step 304 in the first algorithm or step 404 in the second algorithm, the process may proceed to step 508. In step 508, the signal strength in the configuration with the 0-th radiation pattern, S⁰, is measured over a certain time period Δt, and the average of S⁰ over Δt is obtained as Sav⁰. After the radiation pattern is changed to the next pattern in step 512, the signal strength in the new configuration with the K-th radiation pattern, S^(K), is measured over a certain time period Δt, and the average of S^(K) over Δt is obtained as Sav^(K) in step 516. Using the previous measurement value Sav⁰, the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern can be computed as in Eq. (2), i.e., Δav^(K)=Sav^(K)−Sav^(K−1), in step 520. Thereafter, the process proceeds to step 324 in the first algorithm or step 424 in the second algorithm.

Additionally or alternatively, the change of signal strength between measurements can be taken into account by varying the parameter Tshld in the second algorithm according to the magnitude of the signal strength change over a certain time period. FIG. 6 is a flowchart illustrating the procedure for taking signal strength changes into account, which can be incorporated in the second algorithm described with reference to FIG. 4. After the radiation pattern is changed to the next pattern in step 412, the signal strength in the new configuration with the K-th radiation pattern, S^(K), is measured over a certain time period Δt, and the minimum and maximum of S^(K) during Δt is obtained as S^(K) min and S^(K) max, respectively, in step 616. The parameter Tshld is then determined according to the magnitude of |S^(K) max−S^(K) min| in step 620. In general, the larger the |S^(K) max−S^(K) min| is, the larger the Tshld value is to accommodate the variation. The process may proceed to step 420 to compute Δ^(K)=S^(K)−S^(K−1) by using the S^(K) and S^(K−1) values, each measured at a predetermined representative time point during Δt. Alternatively, by combining the time average procedure described with reference to FIG. 5, Δav^(K)=Sav^(K)−Sav^(K−1), may be computed by using the Sav^(K) and Sav^(K−1) values, each representing the average of the signal strength over Δt. Furthermore, instead of changing the parameter Tshld according to the magnitude of the signal strength change for each K, a weight factor for Err^(K) (Θ,Φ) may be determined according to the magnitude of the signal strength change for each K, and multiplied to Err^(K) (Θ,Φ) for the comparison with a fixed Tshld in step 436 of FIG. 4.

Some protocols such as WCDMA use an architecture including a RAKE receiver, which can be utilized in the above algorithms to increase the accuracy of the AOA estimation. In many instances of RF communication, the line of sight between a transmitter and a receiver becomes blocked or shadowed with obstacles such as walls, trees and other objects. Each signal bounce may introduce phase shifts, time delays, attenuations and distortions, giving rise to multipath components of the signal. The multipath components are delayed copies of the original signal travelling through different echo paths, each with a different magnitude and time of arrival at the receiver. Since each component contains original information, the information can be obtained reliably by taking into account the magnitude and time of arrival (phase) of each component.

A RAKE receiver has multiple “fingers,” each assigned to receive a different multipath component. The information obtained by all fingers is correlated to make the best use of the different characteristics of the multipath signals. FIG. 7 illustrates an example schematically showing multipath signals and a communication device receiving them. In this example, the communication device is equipped with a modal antenna coupled with a RAKE receiver. The modal antenna is set with the K-th radiation pattern, and the RAKE receiver is receiving the main signal S^(K) ₁, the first copy S^(K) ₂ of S^(K) ₁, and the second copy S^(K) ₃ of S^(K) ₁. The first copy S^(K) ₂ is a multipath component of the main signal with a bounce before incoming to the communication device, and the second copy S^(K) ₃ is a multipath component of the main signal with a different bounce before incoming to the communication device. The time of arrival of S^(K) ₂ is delayed later than S^(K) ₁, and the time of arrival of S^(K) ₃ is further delayed than S^(K) ₂ in this example.

It is known to those skilled in the art that most of the channel propagation based on the 3GPP standard includes at least one multipath component that arrives at an angle close to the main signal, e.g., within 15 degrees. This fact indicates that if at least one of the components has the incident angle that is close within a certain tolerance to the incident angle of the main signal, the probability is high for the incident angle to be indeed the AOA. Thus, detection of multipath component signals can be utilized to enhance the accuracy, or the confidence level, of the AOA estimation in direction finding algorithms.

FIG. 8 is a flowchart illustrating an algorithm in which multipath components are utilized to enhance the accuracy, or the confidence level, of the AOA estimation in the first algorithm described earlier with reference to FIG. 3, where the angle that gives the minimum of Err(Θ,Φ) is obtained as the AOA of the signal. This example is based on a device including a modal antenna having N modes corresponding to N radiation patterns, and a RAKE receiver coupled to the modal antenna and configured to receive a main signal and two multipath components, i.e., two copies of the main signal. It should be understood that the RAKE receiver can be configured to receive a main signal and one or more copies of the main signal, depending on computation time and other factors. In FIG. 8, the initialization is carried out in step 804, to set the mode, i.e., the radiation pattern of the modal antenna, to be K=0. Additionally, in this step, the discrete values of (Θ,Φ) to span in the spherical coordinate are determined according to the required resolution, and stored in Set{Θ,Φ}. In step 808, the signal strengths of the main signal, the first copy of the main signal and the second copy of the main signal in the configuration with the 0-th radiation pattern, S⁰ ₁, S⁰ ₂, S⁰ ₃, are measured. Steps 812-828 represent the do-loop to compute Err^(K) ₁(Θ,Φ), Err^(K) ₂(Θ,Φ), Err^(K) ₃(Θ,Φ) iteratively from K=1 to K=N, where Err^(K) ₁(Θ,Φ), Err^(K) ₂(Θ,Φ), Err^(K) ₃(Θ,Φ) are defined as in Eq. (3) based on the signal strengths of the main signal, the first copy of the main signal and the second copy of the main signal S^(K) ₁, S^(K) ₂, S^(K) ₃ in the configuration with the K-th radiation pattern. Specifically, after the radiation pattern is changed to the next pattern in step 812, the signal strengths of the main signal, the first copy of the main signal and the second copy of the main signal in the new configuration with the K-th radiation pattern, S^(K) ₁, S^(K) ₂, S^(K) ₃, are measured in step 816. Using the previous measurement values, S^(K−1) ₁, S^(K−1) ₂, S^(K−1) ₃ the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern can be computed for each signal as in Eq. (2), i.e., Δ^(K) _(i)=S^(K) _(i)−S^(K−1) _(i), where i=1, 2 and 3, in step 820. Using the measured signal strength variations Δ^(K) _(i), and the premeasured and stored G^(K)(Θ, Φ) value, which is the gain of the modal antenna at the angle (Θ,Φ) when the K-th radiation pattern is selected, step 824 proceeds to compute Err^(K) _(i)(Θ,Φ) for each i as in Eq. (3), i.e., Err^(K) _(i)(Θ, Φ)=[E^(K)(Θ,Φ)−Δ^(K) _(i)]², where i=1, 2 and 3 and E^(K)(Θ, Φ)=G^(K)(Θ,Φ)−G^(K−1)(Θ,Φ) which is the gain variation, as in Eq. (1). In step 824, this computation is carried out for each pair of (Θ, Φ) values in Set{Θ,Φ}. After the computation of Err^(K)(Θ,Φ) for each pair of (Θ, Φ) values for K=1 through N, in step 832, Err^(K) ₁(Θ,Φ), Err^(K) ₂(Θ,Φ), Err^(K) ₃(Θ,Φ) for all configurations with different radiation patterns is summed as in Eq. (4) to obtain Err₁(Θ,Φ), Err₂(Θ,Φ), Err₃(Θ,Φ) for each pair of (Θ, Φ) values in Set{Θ,Φ}. In step 836, among Erri(Θ, Φ) values for all pairs of (Θ, Φ) in Set{Θ,Φ}, Erri(Θ,Φ) that gives the minimum is found for each of i=1, 2 and 3. Thus, the (Θ, Φ) value that gives the minimum Erri(Θ,Φ) is obtained as the AOA (Θ_(0i), Φ_(0i)) for each of i=1, 2 and 3. In step 838, it is judged if (Θ₀₁,Φ₀₁)=(Θ₀₂, Φ₀₂) and (Θ₀₁, Φ₀₁)=(Θ₀₃, Φ₀₃) within a certain tolerance. If No in this step, it means there is abnormality, and the process goes back to the initialization in step 804. If Yes, it can be determined that the angle (Θ₀₁, Φ₀₁) is the AOA with the high confidence level, and the process proceeds to step 840. If the process is determined to be continued in step 840, the process goes back to step 804 for initialization, and the subsequent steps are repeated. If the process is determined to end, the angle (Θ₀₁, Φ₀₁) is outputted as the AOA in step 844.

Similar to the above, the multipath component signals can be utilized to enhance the accuracy, or the confidence level, of the AOA estimation in the second algorithm described earlier. FIG. 9 is a flowchart illustrating an algorithm in which multipath components are utilized to enhance the accuracy, or the confidence level, of the AOA estimation in the second algorithm described earlier with reference to FIG. 4, where the angle that gives the minimum Err^(K)(Θ,Φ) is obtained as the AOA of the signal for the K-th mode, where the angle (Θ,Φ) is selected from a limited set of angles that satisfy certain criteria. The initialization is carried out in step 904, to set the mode, i.e., the radiation pattern of the modal antenna, to be K=0. Additionally, in this step, the discrete values of (Θ, Φ) to span in the spherical coordinate are determined according to certain criteria, and stored in Subset{Θ,Φ}. The angles (Θ,Φ) in the initial Subset{Θ,Φ} may be selected from the original Set{Θ,Φ} according to an empirical judgment based on the prior computational results or measured data or other sound engineering judgment. In step 908, the signal strengths of the main signal, the first copy of the main signal and the second copy of the main signal in the configuration with the 0-th radiation pattern, S⁰ ₁, S⁰ ₂, S⁰ ₃, are measured. After the radiation pattern is changed to the next pattern in step 912, the signal strengths of the main signal, the first copy of the main signal and the second copy of the main signal in the new configuration with the K-th radiation pattern, S^(K) ₁, S^(K) ₂, S^(K) ₃, are measured in step 916. Using the previous measurement values, S^(K−1) ₁, S^(K−1) ₂, S^(K−1) ₃ the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern can be computed for each signal as in Eq. (2), i.e., Δ^(K) _(i)=S^(K) _(i)−S^(K−1) _(i), where i=1, 2 and 3, in step 920. In step 924, the first pair of (Θ, Φ) is selected from Subset{Θ,Φ}. Using the measured signal strength variations Δ^(K) _(i) and the premeasured and stored G^(K)(Θ, Φ) value, which is the gain of the modal antenna at the angle (Θ,Φ) when the K-th radiation pattern is selected, step 928 proceeds to compute Err^(K) _(i)(Θ,Φ) for each i as in Eq. (3), i.e., Err^(K) _(i)(Θ, Φ)=[E^(K)(Θ,Φ)−Δ^(K) _(i)]², where i=1, 2 and 3 and E^(K)(Θ, Φ)=G^(K)(Θ,Φ)−G^(K−1)(Θ, Φ) which is the gain variation, as in Eq. (1). After the computation of Err^(K) _(i)(Θ,Φ) for the pair of (Θ, Φ), it is judged in step 936 if the Err^(K) _(i)(Θ, Φ) value is smaller than a certain threshold, Tshldi, which is related to a tolerance in judging the accuracy of the final AOA, where i=1, 2 and 3. If Yes, the angle (Θ,Φ) that satisfies the relationships, Err^(K) ₁(Θ, Φ)<Tshld1, Err^(K) ₂(Θ, Φ)<Tshld2, Err^(K) ₃(Θ, Φ)<Tshld3, may be selected and stored in Temp-Subset1{Θ,Φ}, Temp-Subset2{Θ,Φ}, Temp-Subset3 {Θ,Φ}, respectively, in step 940. If No in step 936 as well as after step 940, the process proceeds to step 944, where it is judged if all the angles (Θ, Φ) in Subset{Θ,Φ} have been exhausted. If No in step 944, the next pair of angles (Θ,Φ) in Subset{Θ,Φ} is selected in step 932, and the procedure from step 928 through step 932 is repeated until all the angles (Θ,Φ) in Subset{Θ,Φ} are exhausted. In step 948, Subseti{Θ,Φ} is replaced with Temp-Subseti{Θ,Φ}, which means only the angles (Θ,Φ) that satisfy the relationship, Err^(K) _(i)(Θ,Φ)<Tshldi, are selected and stored as the updated Subseti{Θ,Φ}, where i=1, 2 and 3. In step 950, among Err^(K) _(i)(Θ, Φ) values for all pairs of (Θ, Φ) in Subseti{Θ,Φ}, Err^(K)i(Θ_(0i),Φ_(0i)) that gives the minimum is found for each of i=1, 2 and 3. Thus, the (Θ_(0i),Φ_(0i)) value that gives the minimum Err^(K) _(i)(Θ,Φ) is obtained as the AOA (Θ_(0i),Φ_(0i)) for each of i=1, 2 and 3. In step 952, it is judged if (Θ₀₁, Φ₀₁)=(Θ₀₂, Φ₀₂) and (Θ₀₁, Φ₀₁)=(Θ₀₃, Φ₀₃) within a certain tolerance. If No in this step, it means there is abnormality, and the process goes back to the initialization in step 904; if Yes, it can be determined that the angle (Θ₀₁, Φ₀₁) is the AOA for the K-th mode with the high confidence level, and the process proceeds to step 956. If the process is determined to be continued in step 956, the process proceeds to step 964 to determine if K=N has been reached. If No, the radiation pattern is changed to the next one at step 912, and the subsequent steps are repeated; if Yes, the process goes back to step 904 for initialization, and the subsequent steps are repeated. If the process is determined to end in step 956, the angle (Θ₀₁, Φ₀₁) is outputted as the AOA for the K-th mode in step 960. When the algorithm is repeated from the step 904 or step 912, angles in Subseti{Θ,Φ} defined in step 948 may be used for each of i=1, 2 and 3 in the subsequent steps.

Each of the algorithms described so far with reference to FIGS. 3-9 is configured to obtain the AOA of the incoming signal. After the AOA is found, the algorithm can be repeated for any needed times to update the AOA since the signal incidence may change often or continuously. The information obtained in running the algorithm can be utilized for the next time the same algorithm is driven to run. In particular, the E^(K)(Θ, Φ) values may be updated based on the AOA information previously obtained.

FIG. 10 is a flowchart illustrating the process of updating the E^(K)(Θ, Φ) values, i.e., the gain variations, based on the AOA information previously obtained. Namely, this process represents a post AOA process. After obtaining the AOA (Θ₀, Φ₀) in the first algorithm, the second algorithm or its variation described earlier, the process may proceed to step 1004, where K=0 and (Θ, Φ)=(Θ₀, Φ₀) are set. In step 1008, the signal strength S⁰ in the configuration with the 0-th radiation pattern is measured. After the radiation pattern is changed to the next pattern in step 1012, the signal strength in the new configuration with the K-th radiation pattern, S^(K), is measured in step 1016. Using the previous measurement value S^(K−1), the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern can be computed as in Eq. (2), i.e., Δ^(K)=S^(K)−S^(K−1), in step 1020. The measured signal strength variation Δ^(K) is then stored as E^(K)(Θ₀, Φ₀) in step 1024. Thus, the more accurate E^(K)(Θ₀, Φ₀) value is obtained based on the measured Δ^(K) value, and can be used for the next time the first algorithm, the second algorithm or its variation is driven to run. The above steps are repeated for the next K in step 1028, until all the modes are exhausted. The E^(K)(Θ, Φ) values for the angles (Θ, Φ) other than the angle (Θ₀, Φ₀) may be obtained by using the premeasured and stored G^(K)(Θ, Φ) values. In this way, the E^(K)(Θ, Φ) values for all K's as well as for all angles (Θ, Φ) are initialized for running the algorithm for the next time around with better accuracy. The accuracy in direction finding is expected to go up, as the number of runs increases and E^(K)(Θ, Φ) is updated many times by using the present updating algorithm.

Another post AOA process may be configured to involve decision making as to whether the whole direction finding process should be restarted. In this process, the difference between the signal strength variation, i.e., Δ^(K), and the gain variation at the angle (Θ₀, Φ₀), i.e., E^(K)(Θ₀, Φ₀), can be checked. If the difference is within a certain threshold, it can be determined that the angle (Θ₀, Φ₀) is still close to the AOA; if not, the angle (Θ₀, Φ₀) is no longer the AOA, and thus the complete direction finding process may be restarted. FIG. 11 is a table illustrating an example of gain variations and signal strength variations used for the decision making. The gain variation at the angle (Θ₀, Φ₀) can be E^(K)(Θ₀, Φ₀)=G^(K)(Θ₀,Φ₀)−G^(K−1)(Θ₀,Φ₀) as in Eq. (1), or an average of E^(K)(Θ₀, Φ₀) values obtained after running several times the direction finding algorithm with the updating process illustrated in FIG. 10. The signal strength variation is Δ^(K)=S^(K)−S^(K−1) as in Eq. (2), which is a measured value. In the first step of this table, the previous mode 0 and the current mode 1 are selected, the gain variation at (Θ₀, Φ₀) is obtained to be −2.10 dB, and the Δ^(K) is measured to be −1.50 dB. In the second step of this table, the previous mode 0 and the current mode 2 are selected, the gain variation at (Θ₀, Φ₀) is obtained to be −1.05 dB, and the Δ^(K) is measured to be −3.50 dB. In the third step of this table, the previous mode 1 and the current mode 2 are selected, the gain variation at (Θ₀, Φ₀) is obtained to be −4.20 dB, and the Δ^(K) is measured to be −4.10 dB. By using a predetermined threshold value of 0.7 dB, for example, it is observed that the difference between the gain variation and the signal strength variation in the second step is larger than the threshold value. Thus, it can be determined that the signal direction has changed, and the full direction finding process be restarted to find the new AOA.

The direction finding algorithms described thus far utilize the gain of the modal antenna with the K-th radiation pattern at the angle (Θ,Φ), denoted as G^(K)(Θ,Φ), following Eqs. (1)-(3). As explained earlier, the gain value for each radiation pattern at each selected angle can be premeasured and stored in the memory to be used for the algorithms, and updated as the direction finding processes are being carried out. The accuracy of the direction finding may be enhanced by explicitly including the phase information associated with the gain and the measured signal strength. In this case, Eqs. (1)-(3) take their corresponding complex forms, where the phase of the gain with the K-th radiation pattern is denoted by φ^(K), and j is defined as the imaginary unit. Here, the phase φ^(K) of the gain is a function of two angles, Θ and Φ, in the spherical coordinate, but the notation is simplified in the following equations. The phase φ^(K) of the gain of the modal antenna can be premeasured and stored in the memory for each radiation pattern and for each selected angle. The complex gain variation E^(K)(Θ,Φ) exp(jφ^(K)) denotes the difference in gain between the current mode having the K-th radiation pattern and the previous mode having the (K−1)-th radiation pattern at the angle (Θ,Φ), and is defined as follows: E ^(K)(Θ,Φ)exp(jφ ^(K))=G ^(K)(Θ,Φ)exp(jφ ^(K))−G ^(K−1)(Θ,Φ)exp(jφ ^(K−1)).  Eq. (6) The complex signal strength variation Δ^(K) exp(jβ^(K)) denotes the difference in signal strength between the configurations with the K-th radiation pattern and the (K−1)-th radiation pattern, now including the phase β^(K) representing the measured phase of the signal S^(K), and is defined as follows: Δ^(K)exp(jβ ^(K))=S ^(K)exp(jβ ^(K))−S ^(K−1)exp(jβ ^(K−1)).  Eq. (7) The difference between the complex gain variation and the complex signal strength variation is expressed as follows: Err^(K)(Θ,Φ)=∥E ^(K)(Θ,Φ)exp(jφ ^(K))−Δ^(K)exp(jβ ^(K))∥².  Eq. (8) Note that because the modulus squared operator (∥ ∥²) is used for the complex difference in Eq. (8), the Err^(K)(Θ,Φ) becomes entirely real. Thus, the scalar form of the error metric Err^(K)(Θ,Φ) may be used in Eqs. (1)-(3) even for the present complex case; however, in each of the direction finding algorithms, the complex form as expressed in Eqs. (6)-(8) may be substituted.

The phase β^(K) of the signal S^(K) in Eq. (7) can be obtained from the phase shift measurement. FIG. 12 schematically illustrates the measurement of the phase shift of the signal strength during the transition from the (K−1)-th mode to the K-th mode. The top figure illustrates an example of a received signal waveform, where the in-phase (I) component and the quadrature-phase (Q) component are measured. The mode transition is occurring at the time point indicated by an arrow, and the phase shift is observed at the point. By carrying out the analog-to-digital conversion, the amount of phase shift is obtained as illustrated in the bottom figure. This information is used to obtain β^(K) and β^(K−1) in Eq. (7).

Similar to the gain values used in the previous direction finding algorithms, the phase φ^(K) of the gain of the modal antenna in Eq. (6) can be obtained based on the data that has been premeasured and stored in a memory, such as in the form of a look-up table. FIG. 13 illustrates a portion of the look-up table showing the phase data of the gain according to the angles (Θ, Φ) and the modes, i.e., radiation patterns, K=0 through (N−1). The stored data can be used to obtain φ^(K) and φ^(K−1) in Eq. (6). The phase data can be updated as the direction finding processes are being carried out, and used for the algorithms for enhanced accuracy.

While this document contains many specifics, these should not be construed as limitations on the scope of an invention or of what may be claimed, but rather as descriptions of features specific to particular embodiments of the invention. Certain features that are described in this document in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be exercised from the combination, and the claimed combination may be directed to a subcombination or a variation of a subcombination. 

What is claimed is:
 1. A method for obtaining a direction of a signal incoming to a communication device, which is provided with a modal antenna having a plurality of modes corresponding to a plurality of radiation patterns, respectively, the method comprising: obtaining a gain of the modal antenna at each of predetermined angles for each of the plurality of radiation patterns; first computing a first difference in gain at each of the predetermined angles between each selected pair of the plurality of radiation patterns to obtain a gain variation; measuring a signal strength in a configuration with each of the plurality of radiation patterns; second computing a second difference in signal strength between configurations with each selected pair of the plurality of radiation patterns to obtain a signal strength variation; third computing a third difference between the first difference and the second difference for each of the predetermined angles and for each selected pair of the plurality of radiation patterns; summing a plurality of third differences over all selected pairs of the plurality of radiation patterns to have a value for each of the predetermined angles; and determining an angle of arrival (AOA) of the signal, the AOA giving a minimum among a plurality of values obtained for the predetermined angles, respectively, in the summing wherein: the measuring the signal strength comprises measuring a main signal strength and one or more multipath component signal strengths; the second computing the second difference comprises second computing a main signal strength difference and each of one or more multipath component signal strength differences between configurations with each selected pair of the plurality of radiation patterns; the third computing the third difference comprises third computing a third difference associated with the main signal between the first difference and the main signal strength difference, and one or more third differences associated with the one or more multipath component signals, respectively, between the first difference and the one or more multipath component signal strength differences, respectively, for each of the predetermined angles and for each selected pair of the plurality of radiation patterns; the summing the plurality of third differences over all selected pairs of the plurality of radiation patterns comprises summing a plurality of third differences associated with the main signal over all selected pairs of the plurality of radiation patterns to have a value associated with the main signal for each of the predetermined angles, and summing a plurality of third differences associated with each of the one or more multipath component signals over all selected pairs of the plurality of radiation patterns to have a value associated with each of the one or more multipath component signals for each of the predetermined angles; and the determining the AOA comprises: finding a temporary AOA associated with the main signal, which gives a minimum among a plurality of values associated with the main signal obtained for the predetermined angles, respectively, in the summing, and a temporary AOA associated with each of the one or more multipath component signals, which gives a minimum among a plurality of values associated with each of the one or more multipath component signals obtained for the predetermined angles, respectively, in the summing; judging if the temporary AOA associated with the main signal and the temporary AOA associated with each of the one or more multipath component signals are within a predetermined tolerance; if yes in the judging, determining the temporary AOA associated with the main signal to be the AOA; and if no in the judging, repeating the obtaining through the determining.
 2. The method of claim 1, wherein the gain of the modal antenna at each of the predetermined angles for each of the plurality of radiation patterns is premeasured under various conditions or environments, and stored in a memory according to the various conditions or environments.
 3. The method of claim 2, wherein the obtaining the gain comprises: sensing the condition or environment using one or more sensors during a time interval; and selecting the gain in the memory according to the sensed condition or environment.
 4. The method of claim 1, further comprising: updating the first difference in gain at each of the predetermined angles between each selected pair of the plurality of radiation patterns to update the gain variation for use when the obtaining through the determining are repeated.
 5. The method of claim 4, wherein the updating comprises: second measuring an updating signal strength in a configuration with each of the plurality of radiation patterns; fourth computing a difference in updating signal strength between configurations with each selected pair of the plurality of radiation patterns to obtain an updating signal strength variation; first storing the updating signal strength variation as the gain variation between each selected pair of the plurality of radiation patterns at the AOA; and second storing a difference in gain at each of the predetermined angles other than the AOA between each selected pair of the plurality of radiation patterns based on premeasured gains to update the gain variation at each of the predetermined angles other than the AOA.
 6. The method of claim 1, further comprising: decision making as to whether the obtaining through the determining be repeated.
 7. The method of claim 6, wherein the decision making comprises: second obtaining a difference between the gain variation at the AOA between a selected pair of the plurality of radiation patterns and the signal strength variation between configurations with the selected pair of the plurality of radiation patterns; judging if the difference is larger than or smaller than a predetermined threshold; making decision to repeat the obtaining through the determining if the difference is larger than the predetermined threshold.
 8. The method of claim 7, wherein the gain variation at the AOA between the selected pair of the plurality of radiation patterns is the first difference in gain at the AOA between the selected pair of the plurality of radiation patterns.
 9. The method of claim 7, wherein the gain variation at the AOA between the selected pair of the plurality of radiation patterns is an average of a plurality of the first differences in gain at the AOA between the selected pair of the plurality of radiation patterns, wherein one or more of the plurality of the first differences are obtained based on an updating procedure prior to the averaging.
 10. The method of claim 1, wherein the main signal strength and the one or more multipath component signals are measured by using a rake receiver coupled to the modal antenna.
 11. The method of claim 1, wherein the obtaining the gain of the modal antenna comprises obtaining the gain including a phase of the gain at each of predetermined angles for each of the plurality of radiation patterns; and the measuring the signal strength comprises obtaining the signal strength including a phase of the signal strength in a configuration with each of the plurality of radiation patterns, based on a phase shift measurement.
 12. A method for obtaining a direction of a signal incoming to a communication device, which is provided with a modal antenna having a plurality of modes corresponding to a plurality of radiation patterns, respectively, the method comprising: obtaining a gain of the modal antenna at each of predetermined angles for each of the plurality of radiation patterns; first computing a first difference in gain at each of the predetermined angles between each selected pair of the plurality of radiation patterns to obtain a gain variation; measuring a signal strength in a configuration with each of the plurality of radiation patterns; second computing a second difference in signal strength between configurations with each selected pair of the plurality of radiation patterns to obtain a signal strength variation; third computing a third difference between the first difference and the second difference for each of the predetermined angles and for each selected pair of the plurality of radiation patterns; judging if the third difference is less than a predetermined threshold for each of the predetermined angles for each selected pair of the plurality of radiation patterns; storing the angle as one of the predetermined angles if the third difference is less than the predetermined threshold for each of the predetermined angles for each selected pair of the plurality of radiation patterns; and determining an angle of arrival (AOA) of the signal, the AOA giving a minimum among a plurality of third differences obtained for the predetermined angles, respectively, in the third computing, for each pair of the plurality of radiation patterns, the predetermined angles being obtained in the storing; wherein: the measuring the signal strength comprises measuring a main signal strength and one or more multipath component signal strengths; the second computing the second difference comprises second computing a main signal strength difference and each of one or more multipath component signal strength differences between configurations with each selected pair of the plurality of radiation patterns; the third computing the third difference comprises third computing a third difference associated with the main signal between the first difference and the main signal strength difference, and one or more third differences associated with the one or more multipath component signals, respectively, between the first difference and the one or more multipath component signal strength differences, respectively, for each of the predetermined angles and for each selected pair of the plurality of radiation patterns; the judging comprises judging, for each of the predetermined angles for each selected pair of the plurality of radiation patterns, if the third difference associated with the main signal is less than a predetermined threshold, and if each of the one or more third differences associated respectively with the one or more multipath component signals is less than a predetermined threshold; the storing comprises storing, for each of the predetermined angles for each selected pair of the plurality of radiation patterns, the angle as one of the predetermined angles associated with the main signal if the third difference associated with the main signal is less than the predetermined threshold, and the angle as one of the predetermined angles associated with each of the one or more multipath component signals if the third difference associated with each of the one or more multipath component signals is less than the predetermined threshold; and the determining the AOA comprises: first finding a temporary AOA associated with the main signal, which gives a minimum among a plurality of third differences associated with the main signal, the plurality of third differences obtained for the predetermined angles, respectively, in the third computing, for each pair of the plurality of radiation patterns, the predetermined angles being the predetermined angles associated with the main signal obtained in the storing; second finding a temporary AOA associated with each of the one or more multipath component signals, which gives a minimum among a plurality of third differences associated with each of the one or more multipath component signals, the plurality of third differences obtained for the predetermined angles, respectively, in the third computing, for each pair of the plurality of radiation patterns, the predetermined angles being the predetermined angles associated with each of the one or more multipath component signals obtained in the storing; second judging if the temporary AOA associated with the main signal and the temporary AOA associated with each of the one or more multipath component signals are within a predetermined tolerance; if yes in the second judging, determining the temporary AOA associated with the main signal to be the AOA; and if no in the second judging, repeating the obtaining through the determining.
 13. The method of claim 12, wherein the gain of the modal antenna at each of the predetermined angles for each of the plurality of radiation patterns is premeasured under various conditions or environments, and stored in a memory according to the various conditions or environments.
 14. The method of claim 13, wherein the obtaining the gain comprises: sensing the condition or environment using one or more sensors during a time interval; and selecting the gain in the memory according to the sensed condition or environment.
 15. The method of claim 12, further comprising: updating the first difference in gain at each of the predetermined angles between each selected pair of the plurality of radiation patterns to update the gain variation for use when the obtaining through the determining are repeated.
 16. The method of claim 15, wherein the updating comprises: second measuring an updating signal strength in a configuration with each of the plurality of radiation patterns; fourth computing a difference in updating signal strength between configurations with each selected pair of the plurality of radiation patterns to obtain an updating signal strength variation; first storing the updating signal strength variation as the gain variation between each selected pair of the plurality of radiation patterns at the AOA; and second storing a difference in gain at each of the predetermined angles other than the AOA between each selected pair of the plurality of radiation patterns based on premeasured gains to update the gain variation at each of the predetermined angles other than the AOA.
 17. The method of claim 12, further comprising: decision making as to whether the obtaining through the determining be repeated.
 18. The method of claim 17, wherein the decision making comprises: second obtaining a difference between the gain variation at the AOA between a selected pair of the plurality of radiation patterns and the signal strength variation between configurations with the selected pair of the plurality of radiation patterns; second judging if the difference is larger than or smaller than a second predetermined threshold; making decision to repeat the obtaining through the determining if the difference is larger than the second predetermined threshold.
 19. The method of claim 18, wherein the gain variation at the AOA between the selected pair of the plurality of radiation patterns is the first difference in gain at the AOA between the selected pair of the plurality of radiation patterns.
 20. The method of claim 18, wherein the gain variation at the AOA between the selected pair of the plurality of radiation patterns is an average of a plurality of the first differences in gain at the AOA between the selected pair of the plurality of radiation patterns, wherein one or more of the plurality of the first differences are obtained based on an updating procedure prior to the averaging.
 21. The method of claim 12, wherein the main signal strength and the one or more multipath component signals are measured by using a rake receiver coupled to the modal antenna.
 22. The method of claim 12, wherein the obtaining the gain of the modal antenna comprises obtaining the gain including a phase of the gain at each of predetermined angles for each of the plurality of radiation patterns; and the measuring the signal strength comprises obtaining the signal strength including a phase of the signal strength in a configuration with each of the plurality of radiation patterns, based on a phase shift measurement. 